Tagged Questions

Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also ...

According to the paper "Faster addition and doubling on elliptic curves" by Bernstein and Lange, the Montgomery curve (Curve25519) $$v^{2}=u^{3}+486662\cdot u^{2}+u$$ is birationally equivalent to the ...

I would like to know how to compute multiplication of two valid EC points over a curve E with generator G.
i.e. Given only P and Q points then how to compute R = P * Q
where $P = p G$, $Q = q G$ and ...

Point multiplication using Montgomery ladder technique over Montgomery curves only require x coordinate, which in many situation leads to faster implementation as compared to point multiplication over ...

What is the benefit of using elliptic curves over the standard finite field, when the cyclic subgroup we consider of the EC's solution group is just isomorphic to some integer residue class of prime ...

It appears that the conditions for applicability of Elligator-2 against many of the SaveCurves curves, where $q \mod 4 = 3$ will inevitably poke a hole in the bit-string set over $(0, 1, .. (q-1)/2)$.
...

My goal is to allow two clients to send files securely over an untrusted network without the need for more than one block of information to be sent. Both clients have ECDSA keys of size 256 bits. I'd ...

Why does EdDSA use the (SHA512) hash of the secret key as the exponent for the public key rather than using the secret key value directly? This seems inefficient and I can't see how it adds any extra ...

As far as I know non pairing pairing based cryptography is less time consuming than pairing based because, pairing based uses complex operations. Are there any advantages of pairing based cryptography ...

I will be giving a short (10-15 min) presentation on the fundamentals of elliptic curve cryptography, and I would like some suggestions on how to show the basic workings of asymmetric key exchange on ...

Are there any optimised implementations of the Supersingular Isogeny Key Exchange by Defeo, Jao, and Plut. It seems like this would be a great drop-in replacement for Diffie-Hellman in both OpenSSL ...

I am wondering if there is a feasible way that, given a specific elliptic curve (such as secp256r1), I could create a keypair where the public key has a given $x$-coordinate. If it is not possible, is ...

I was reading the Wikipedia article on Post Quantum Cryptography and was interested in opinions as to whether the Supersingular Elliptic Curve Isogeny Diffie-Hellman listed there would be a good Post ...

I was looking the certificate of this website: https://www.cloudflare.com that has an ECC based certification.
I'm just curious to know if is possible to understand which elliptic curve is used and ...

A quick question, we know that raw RSA is a no go. To solve this we have different PKCS standards forcing structure on the input messages.
For EC the story is something else. For signatures we have ...

Daniel J. Bernstein (and others) have expressed concern over how "verifiably random" curve parameters are generated. He points out that hashing a public seed doesn't prevent, say, the US government ...

Are ring signatures possible with elliptic curves? If so how. The original paper by Rivest, Shamir, Tauman seems to require an invertible trapdoor function. But I've only seen algorithms for secret ...

Bruce Schneier and Gregory Maxwell have both stated that they believe the constants chosen for NIST's P curves (i.e. P-256r) are cooked. DJB has put together a detailed list of red flags but, outside ...

I'm writing a coursework and right now I've implemented the ECDSA algorithm, but I also need to encrypt and decrypt small text files (.txt) using elliptic curve cryptography.
The problem is that I do ...

In ECDH protocol is possible, naturally, to use the same algorithm for calculate a secret key for both communication parties (Alice and Bob for example). It is possible to design also a same algorithm ...

I want to get a group element $h$ on the elliptic curve secp256k1. The important thing is that no one should know the discrete logarithm of $h$ with respect to $g$. That is, $h$ should be created from ...

I am studying (sliding) window method in Elliptic Curve Cryptography (ECC) but I am confused by the term, signed fixed window method. By the way term is used in a research paper and not in the book ...